The game is gated in a way so if you have enough SOULS, you will prob have enough anima to make that building. But I don;t have enough souls on my main, that I log every day since launch, so why would you expect yo have 10k anima on an alt, as soon as you ding ?
On my alt, dinged on 10.01, I've spent my anima on 2x tier 1 (transport + command table) and the rest of the anima went to upgrading covenant gear.
I could have build 1 tier 2, I have only 8 souls remaining. But that's just the game, you make decisions if you wanna gear an alt faster or have a tier 2 covenant building.
I mean, renown 19 + ilvl 179 + Torghast 1x L8 + 1x L7 cleared + Legendary + the fact I haven't done any dungeons, except the one I was forced to do from the covenant quest line .. I'd say it is not to bad for an alt that dinged 2 days ago.
You problem with anima just seems you want it all NOW.